What is the limit as x approaches infinity of (5-2x^{3/2})/(3x-4) ?

The limit as x approaches infinity of (5-2x^{3/2})/(3x-4) is -infinity

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limit as x approaches infinity of (5-2x^{3/2})/(3x-4)

x \to \infty lim (\frac{5 - 2 x ^{\frac{3}{2}}}{3 x - 4})

- \infty

Solution steps

x \to \infty lim (\frac{5 - 2 x ^{\frac{3}{2}}}{3 x - 4})

Divide by highest denominator power:

\frac{\frac{5}{x} - 2 x ^{\frac{1}{2}}}{3 - \frac{4}{x}}

= x \to \infty lim (\frac{\frac{5}{x} - 2 x ^{\frac{1}{2}}}{3 - \frac{4}{x}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to \infty} ( \frac{5}{x} - 2 x ^{\frac{1}{2}} )}{lim _{x \to \infty} ( 3 - \frac{4}{x} )}

x \to \infty lim (\frac{5}{x} - 2 x^{\frac{1}{2}}) = - \infty

x \to \infty lim (3 - \frac{4}{x}) = 3

= \frac{- \infty}{3}

Apply Infinity Property:

\frac{- \infty}{c} = - \infty

= - \infty

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What is the limit as x approaches infinity of (5-2x^{3/2})/(3x-4) ?
The limit as x approaches infinity of (5-2x^{3/2})/(3x-4) is -infinity